Computations of SIFs for Non-Symmetric V-Notched Plates by the FFEM

2009 ◽  
Author(s):  
Muhammad Treifi ◽  
S. Olutunde Oyadiji
Keyword(s):  
Analytical Solutions ◽  
Processing Technique ◽  
Published Data ◽  
Exact Analytical Solutions ◽  
Singular Region ◽  
Small Set ◽  
Notch Tip ◽  
Nodal Displacements ◽  
Global Stiffness Matrix ◽  
Generalised Coordinates

The present paper further develops The Fractal-like Finite Element Method (FFEM) to compute the stress intensity factors (SIFs) for non-symmetrical configurations of sharp V-notched plates. The use of global interpolation functions (GIFs) in the FFEM significantly reduces the number of unknown variables (nodal displacements) in a singular region surrounding a singular point to a small set of generalised coordinates. The same exact analytical solutions of the notch tip asymptotic field derived for a symmetrical notch case can be used as GIFs when the notch is non-symmetrical. However, appropriate local coordinate transformation in the singular region is required to obtain the correct global stiffness matrix. Neither post-processing technique to extract SIFs nor special singular elements to model the singular region are required. Any conventional finite elements can be used to model the singular region. The SIFs are directly computed because of the use of exact analytical solutions as GIFs whose coefficients (generalised coordinates) are the unknowns in the singular region. To demonstrate the accuracy and efficiency of the FFEM to compute the SIFs and model the singularity at a notch tip of non-symmetrical configurations of notched plates, various numerical examples are presented and results are validated via available published data.

scholarly journals A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ji Juan-Juan ◽  
Guo Ye-Cai ◽  
Zhang Lan-Fang ◽  
Zhang Chao-Long
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Space Time ◽  
Hyperbolic Function ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Table Lookup ◽  
Exact Analytical Solutions ◽  
Function Solution

A table lookup method for solving nonlinear fractional partial differential equations (fPDEs) is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1)-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

scholarly journals Modelling Activity and Durability of Electrocatalysts from a Statistical Perspective

2021 ◽  
Author(s):  
Jun Huang
Keyword(s):  
Exponential Decay ◽  
Analytical Solutions ◽  
Electrocatalytic Activity ◽  
Active Sites ◽  
Simple Theory ◽  
Exact Analytical Solutions ◽  
Modelling Activity ◽  
Closing The Gap ◽  
The Mean ◽  
Kinetics Of

<p>We develop a theory to investigate how energetic nonhomogeneity of active sites determines the overall activity of an electrocatalyst and how the evolution of the nonhomogeneity determines the overall durability. The simple theory is amenable to exact analytical solutions and thus fosters an in-depth transparent analysis. It is revealed that nonhomogeneity does not necessarily diminish the electrocatalytic activity; instead, the highest overall activity is obtained with a suitable level of nonhomogeneity that is commensurate with the mean property. The evolution kinetics of nonhomogeneity is described by using the Fokker-Planck theory. Exponential decay of the activity is predicted theoretically and confirmed experimentally. The present work represents a first step toward closing the gap between model and practical electrocatalysts using statistical considerations.</p>

INFLATIONARY SCENARIO IN BRANS–DICKE THEORY FOR BIANCHI VI0 SPACE–TIME MODEL

2003 ◽  
Vol 12 (01) ◽  
pp. 129-143 ◽  
Author(s):  
SUBENOY CHAKRABORTY ◽  
ARABINDA GHOSH
Keyword(s):  
Equation Of State ◽  
Perfect Fluid ◽  
Analytical Solutions ◽  
Fluid Model ◽  
Space Time ◽  
Time Model ◽  
Exact Analytical Solutions ◽  
Exponential Expansion ◽  
Barotropic Equation ◽  
Space Time Model

We have investigated perfect fluid model in Brans–Dicke theory for Bianchi VI 0 space–time and have obtained exact analytical solutions considering barotropic equation of state. These solutions have been analyzed for different values of the parameters involved and some of them have shown a period of exponential expansion.

scholarly journals Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Adel Al-Rabtah ◽  
Shaher Momani ◽  
Mohamed A. Ramadan
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Spline Functions ◽  
Exact Analytical Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Good Agreement

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for0<α≤1andα≥1, whereαdenotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented elsewhere. Results also show that the technique introduced here is robust and easy to apply.

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